# Diffusing in the Right Space: A Systematic Study of Latent Diffusability

arXiv: https://arxiv.org/abs/2606.03578 · HTML: https://mlsanity.com/paper/2606.03578/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 22 of its 34 references that are in the map.
- First posted on arXiv 2 Jun 2026.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 22 of 22)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [Masked Autoencoders Are Scalable Vision Learners](https://mlsanity.com/paper/2111.06377/) (2021)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [An Empirical Study of Training Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.02057/) (2021)
- [Qwen-Image Technical Report](https://mlsanity.com/paper/2508.02324/) (2025)
- [FLUX.1 Kontext: Flow Matching for In-Context Image Generation and Editing in Latent Space](https://mlsanity.com/paper/2506.15742/) (2025)
- [SiT: Exploring Flow and Diffusion-based Generative Models with Scalable Interpolant Transformers](https://mlsanity.com/paper/2401.08740/) (2024)
- [An Image is Worth 32 Tokens for Reconstruction and Generation](https://mlsanity.com/paper/2406.07550/) (2024)
- [Hunyuan-DiT: A Powerful Multi-Resolution Diffusion Transformer with Fine-Grained Chinese Understanding](https://mlsanity.com/paper/2405.08748/) (2024)
- [Large-scale Unsupervised Semantic Segmentation](https://mlsanity.com/paper/2106.03149/) (2021)
- [RADIOv2.5: Improved Baselines for Agglomerative Vision Foundation Models](https://mlsanity.com/paper/2412.07679/) (2024)
- [EQ-VAE: Equivariance Regularized Latent Space for Improved Generative Image Modeling](https://mlsanity.com/paper/2502.09509/) (2025)
- [What matters for Representation Alignment: Global Information or Spatial Structure?](https://mlsanity.com/paper/2512.10794/) (2025)
- [DC-AE 1.5: Accelerating Diffusion Model Convergence with Structured Latent Space](https://mlsanity.com/paper/2508.00413/) (2025)
- [Representation Fr'echet Loss for Visual Generation](https://mlsanity.com/paper/2604.28190/) (2026)
- [Towards Scalable Pre-training of Visual Tokenizers for Generation](https://mlsanity.com/paper/2512.13687/) (2025)
- [An Analytical Theory of Spectral Bias in the Learning Dynamics of Diffusion Models](https://mlsanity.com/paper/2503.03206/) (2025)
- [The Prism Hypothesis: Harmonizing Semantic and Pixel Representations via Unified Autoencoding](https://mlsanity.com/paper/2512.19693/) (2025)
- [Delving into Latent Spectral Biasing of Video VAEs for Superior Diffusability](https://mlsanity.com/paper/2512.05394/) (2025)

## Built on by (most cited first, 6 of 6)

- [KVAE: Family of Tokenizers for Multimodal Generative Models](https://mlsanity.com/paper/2608.05798/) (2026)
- [AffineTok: Semantic Affine Consistency for Diffusion-Friendly Visual Tokenizer](https://mlsanity.com/paper/2608.23864/) (2026)
- [GAE: Learning a Geometry-Native Latent Space for 3D-Consistent World Generation](https://mlsanity.com/paper/2609.24981/) (2026)
- [HiRAE: Hierarchical Representation Autoencoding with Residual Budgets](https://mlsanity.com/paper/2609.37775/) (2026)
- [Token-World: World Modeling in Vision-Language Model Token Space for Robot Manipulation](https://mlsanity.com/paper/2610.00575/) (2026)
- [Image Tokenizers Should Be Trained Between Images](https://mlsanity.com/paper/2610.16759/) (2026)

## Abstract (arXiv)

Latent diffusion models leverage visual tokenizers to compress images into latent spaces for efficient generative modeling. However, better reconstruction quality of a tokenizer does not necessarily translate into better generation quality, suggesting that latent representations should be evaluated not only by fidelity but also by their diffusability. Recent studies have proposed diverse explanations for diffusion-friendly latent spaces, including semantic separability, affine equivariance, distribution uniformity, spatial structure, spectral smoothness, and manifold continuity. Yet these properties are often validated on a limited set of tokenizers, leaving it unclear which factors are most predictive of downstream generation quality and whether such conclusions hold beyond the specific settings in which they are introduced. In this work, we conduct a systematic study of latent diffusability by training a large collection of tokenizers with diverse regularization strategies, architectures, and latent configurations, and evaluating them with multiple downstream diffusion backbones. Our analysis identifies several latent properties that consistently correlate with generation quality and exhibit strong generalization across experimental settings. Beyond existing metrics, we introduce Velocity Irreducible Variance (VIV), a measure of velocity ambiguity induced by trajectory crossings. Extensive experiments show that VIV is one of the most stable predictors of generation quality.